A,B, C denote expressions reperesenting one side of an equation: \[A = 1 \wedge B=1 \rightarrow A=B\]
\[A = 1 \rightarrow A^2=1\]
\[A = 1 \rightarrow A^4=1\]
\[A = 1 \rightarrow A^n=1\]
\[A = 1 \wedge B=1 \rightarrow A/B=1\]
\[A = 1 \wedge B=C-1 \rightarrow B=C-A\]
\[A = 1 \wedge B=1 \rightarrow A-B=0\]
The first rule says for example that if there are two expressions A and B both equalling 1 there is equality between these expressions and thus a new equation can be derived: A=B.
Basically these rules are simple rules for algebraic operations.
The list by now has been extended to those rules which have been applied when deriving the equations on this website.